The cosine hyperbolic-and sine hyperbolic rules for dual hyperbolic spherical trigonometry

Abstract

The dual hyperbolic unit sphere $H^2_0$ is the set of all dual time-like units vectors in the dual Lorentzian space $D^3_1$ with signature (+,+,-). In this paper, we give the cosine hyperbolic and sine hyperbolic-rules for a dual dual hyperbolic spherical triangle $\tilde{A}\tilde{B}\tilde{C}$ which its sides are great-circle-arcs.